A New Empirical Formula for the Aerodynamic Roughness of Water Surface Waves

A new empirical formula for the aerodynamic roughness of water surface waves has been derived from laboratory experimental results using dimensional analysis. The formula has different forms according to wind speed: at moderate wind speeds the formula is a function of the friction velocity of wind, the surface tension, the water density, the kinematic viscosity of water and the acceleration of gravity; at strong winds the formula is expressed by the Charnock relation. The aerodynamic roughness does not depend on such wave state parameters as the spectral peak frequency or the steepness of waves, unlike almost all parameterizations that have been proposed to date. The drag coefficient at moderate winds depends on the surface tension of water and the water temperature through the temperature dependence of the kinematic viscosity of water.     

New Interpretation of Dependence of Wind Stress on Wave State

Based on observations from buoys, it is found that the wave age is well correlated with the nondimensional wave height, and this correlation is best described by a 3/5-power law. This similarity law is valid in the cases of wind waves as well as swells under natural sea states. On the basis of the 3/5-power law combined with the well-known 3/2-power law, it is shown that the wave-induced wind stress increases rapidly with wave age, indicating that the traditional observations or analytic techniques have only given the turbulent Reynolds stress induced by short wind waves, but excluded the long-wave-induced wind stress. The latter constitutes a small fraction to the total wind stress when the wave age is smaller than 1.0. The increase of sea-surface roughness with wave age can be attributed to wave breaking.     

Rainfall effect on wind waves and the turbulence beneath air-sea interface

Rainfall effects on wind waves and turbulence are investigated through the laboratory experiments in a large wind-wave tank. It is found that the wind waves are damped as a whole at low wind speeds, but are enhanced at high wind speeds. This dual effect of rain on the wind waves increases with the increase of rain rate, while the influence of rainfall-area length is not observable. At the low wind speed, the corresponding turbulence in terms of the turbulent kinetic energy （TKE） dissipation rate is significantly enhanced by rain- fall as the waves are damped severely. At the high wind speed, the augment of the TKE dissipation rate is suppressed while the wind waves are enhanced simultaneously. In the field, however, rainfall usually hin- ders the development of waves. In order to explain this contradiction of rainfall effect on waves, a possibility about energy transfer from turbulence to waves in case of the spectral peak of waves overlapping the inertial subrange of turbulence is assumed. It can be applied to interpret the damping phenomenon of gas trans- fer velocity in the laboratory experiments, and the variation of the TKE dissipation rates near sea surface compared with the law of wall.     

粗糙度与风浪特征量关系的研究

在实验室风浪槽中观测风浪和风速,研究粗糙度与波面特征量的关系,发现风浪谱宽度增加,粗糙度增大。在窄谱时,粗糙度随谱宽的增加变化不明显,当波陡降低,粗糙度降低;在宽谱时,当谱宽度增加,即使波陡降低,粗糙度仍可增大。这一结果表明,波陡不足以完全决定粗糙度。当风浪波龄增加,粗糙度呈下降趋势,但由于谱宽度对粗糙度的影响,当波龄增加,部分波浪可有较大的粗糙度。由于这一因素,在粗糙度与波龄关系的观测结果中,数据点的散落不完全由观测误差造成。     

Modulation of short wind waves by a long surface wave: a mechanism for feedback with an air flow

The paper concentrates on the evolution of a spectrum of short wind waves (SW) along the profile of a long surface wave (LW). Short wave spectral variations are considered in the relaxation approximation. The SW spectrum is modulated by the orbital velocities of long waves and by the variations of wind stress along the LW profile. The latter effect occurs due to wind flux perturbations induced by both the long wave proper and variations of the sea surface roughness induced by the SW modulations. To describe this effect, a feedback mechanism is introduces—the growth of energy of short waves results in the larger roughness of the sea surface, thereby contributing to the local wind stress, which facilitates, in turn, the growth of short waves. With moderate and strong winds being involved, this effect (aerodynamic feedback) is shown to be dominant in the short wave spectrum modulation. The mechanism becomes more efficient with intensification of the wind and decreasing of the long waves' frequency. Results of model calculations are in agreement with the known experimental data. Translated by Vladimir A. Puchkin.     

Water-temperature effect on the spectral density of wind gravity waves and on sea-surface roughness

The results of hourly measurements of sea roughness and hydrometeorological parameters, which were automatically taken from special buoys over a long period of time, were used. These buoys were located in the open regions of both the Atlantic and Pacific oceans in different climatic zones; the mean water-surface temperature around the buoys varies from 1–3°C to 26–28°C. In addition to measurement results, the tables contain data on the spectral density of sea roughness for a wide range of frequencies. An analysis of these data, which was made for a short-wave region of the wind-wave spectrum, for the first time revealed a noticeable watertemperature dependence of the spectral density of wind waves within the frequency range 0.30–0.40 Hz, which corresponds to wave lengths of 9-4 m. The presence of such dependence is explained by a rapid temperature change in kinematic sea-water viscosity. Earlier, we indicated the temperature dependence of only very short spectral components that relate to a centimetric wavelength range. The statistical significance of the watertemperature effect on the spectral density of waves of the indicated frequency is supported by the results of a variance analysis. Temperature variations in the parameter of sea-surface roughness, which is determined, first of all, by the energy of the spectral shortwave region, are estimated. Altimetry is the basic method which is used in remotely determining the velocity of near-water wind. This method allows one to obtain records of deviations of the sea surface from the geoid surface and to calculate (on the basis of these records) the spectral density of wave components of almost any frequency. It is known that the wave-spectrum components in the region of low frequencies are almost always affected by ripple. Consequently, the energy of these components is determined not only by wind forcing, and only the components in the range of frequencies exceeding approximately 0.3 Hz are purely windy. Therefore, using the results of sea-surface altimetry in order to determine the velocity of near-water wind, one should use the spectral densities of wave components in this frequency region. The water-temperature dependence of the spectral density of short wind waves is manifested only in a certain frequency interval, which supports this recommendation.     

星载SAR对雨团催生海面风场的观测研究

雨团或对流雨是热带与亚热带地区的主要降雨形式,较易被高分辨率星载合成孔径雷达（SAR）探测到。SAR图像上的雨团足印是由大气中雨滴的散射与吸收、下沉气流等共同导致形成的。本文以RADARSAT-2卫星100 m分辨率的SAR图像上雨团引起的海面风场及其结构反演与解译作为实例进行分析。使用CMOD4地球物理模式函数,分别以NCEP再分析数据、欧洲MetOp-A卫星先进散射计（ASCAT）和中国HY-2卫星微波散射计的风向为外部风向,进行了SAR图像的海面风场反演。反演的海面风速相对于NCEP、ASCAT和HY-2的均方根误差（RMSE）分别为1.48 m/s,1.64 m/s和2.14 m/s。SAR图像上一侧明亮另一侧昏暗的圆形信号图斑被解译为雨团携带的下沉气流对海面风场（海面粗糙度）的改变所致。平行于海面背景风场其通过雨团圆形足印中心的剖面上的风速变化可拟合为正弦或余弦曲线,其拟合线性相关系数均不低于0.80。背景风场的风速大小、雨团引起的风速大小以及雨团足印的直径可利用拟合曲线获得,雨团足印的直径大小一般为数千米或数十千米,本文的8例个例解译与分析均验证了该结论。     

浙江近海典型寒潮浪的数值模拟:以2015年3月和2016年1月为例

本文选用第三代海浪模式SWAN(SimulatingWAveNearshore),以CCMP(Cross-CalibratedMultiPlatform)风场作为驱动风场,数值模拟了2015年3月份和2016年1月份影响浙江省的两次典型寒潮,并将模拟结果与实测数据进行了对比,模拟误差均在20%之内,属于可以接受的范围,表明SWAN模型和CCMP风场能够满足此次寒潮浪数值模拟的需要。本文从风场的强度、最值风速、风向、持续时间等方面,对比了两次寒潮期间的寒潮风场;从寒潮浪的强度、最值波高分布、持续时间、涌浪分布区域等方面,对两次典型寒潮期间的寒潮浪时空分布的异同进行了研究。总体而言,2015年3月份寒潮的风场从强度上弱于2016年1月份寒潮, 3月份寒潮风场的主流大风是6～7级风,风向偏正北风;1月份寒潮风场的主流大风是6～8级风,风向偏西北风。2015年3月份的寒潮浪强度上弱于2016年1月份寒潮浪, 3月份寒潮浪波高变化剧烈的区域位于研究区域的东北部, 1月份寒潮浪波高变化剧烈的区域位于研究区域的中部和东部; 3月份寒潮浪的大浪主要是5级浪, 1月份寒潮浪的大浪主要是5、6级浪。当寒潮对研究区域的波浪场影响最为显著时,2015年3月份寒潮期间研究区域的北部多为涌浪,2016年1月份寒潮期间研究区域的南部多为涌浪。     

Short-wave measurements by a fixed tower-based and a drifting buoysystem

The small-scale roughness of the sea surface acts as an important link in air-sea interaction processes. Radar and sonar waves are scattered by short surface waves providing the basis for remote sensing methods of the sea surface. At high wind speeds, breaking waves occur. Bubbles penetrate into the water and drastically increase acoustical reverberation, transmission loss and ambient noise. Thus, the development of short waves and wave breaking have to be known to apply radar remote sensing to the surface and to deduce from radar backscatter which sonar conditions prevail. To measure the wind dependence of short waves an experimental device was constructed for use from stationary platforms. It is nearly all-weather capable and can easily be handled by a crane. On the other hand, frequencies of short waves measured in a fixed position are extremely frequency shifted by currents. This limits the usefulness of tower-based measurements, e.g., the short wave modulation by wind and waves or currents can only be estimated in a rough approximation. Consequently, a buoy was developed to reduce the frequency shifts. The principle of the buoy is to drift in the local surface current and to follow the amplitudes of long waves. Therefore, short waves are measured in facets of long waves and the Doppler shifts are minimized. The wind is measured at a constant height above the long wave profile and relative to the moving facets. The paper describes the conventional measuring device and points out the necessity of the drifting buoy system. Examples of wind and wave spectra are presented and short wave modulations by long waves are depicted, too. From these measurements, new insights in short wave behaviour have to be expected     

Numerical calculation of drift current in wind waves

-Drift current induced by wind and waves is investigated with phase-averaged Navier-Stokes equation in which the Reynolds stress is closed by k-ε model. The governing equations are solved by the finite volume method in a system of nonorthogonal coordinates which is fitted to the phase-averaged wave surface. The predicted drift current is fairly reasonable and the drag coefficient of sea-surface predicted with the newly developed interface conditions shows good agreement with previous measurements when breaking waves do not exist.     

孟加拉湾局地动力过程的季节变化研究

利用观测资料和理论模型,研究了孟加拉湾海表面高度的季节循环.结果表明,局地风应力旋度驱动的斜压Rossby波是孟加拉湾海表高度季节循环的主要控制因子,而孟加拉湾海底地形分布也影响了海表面高度的季节循环.受风应力旋度驱动的斜压Rossby波在短时间内就可以穿越孟加拉湾海盆,使得海洋温跃层在短时间内完成了对Rossby波的响应,保证了上层海洋满足准静止的Sverdrup平衡.在夏季(冬季)西南(东北)季风驱动下,上层海洋分别在孟加拉湾北部和南部形成气旋(反气旋)式和反气旋(气旋)式环流.     

Influence of wavelength on the parameterization of drag coefficient and surface roughness

Surface waves are the roughness element of the ocean surface, the air-sea interaction processes are influenced by the wave conditions. The dynamic influence of surface waves decays exponentially with distance from the air-water interface. The relevant length scale characterizing the decay rate is the wavelength. The parameterization of drag coefficient and surface roughness can be significantly improved by using wavelength as the reference length scale of atmospheric measurements. The wavelength scaling of drag coefficient and dynamic roughness also receives support from theoretical studies of wind and wave coupling.     

海气动量通量研究综述

海气界面动量通量也称为风应力,是海流和表面海浪的主要驱动力,是海洋从大气获得动量的重要途径。因此,合理可靠的海洋表面风应力的参数化对于海洋、大气和波浪以及气候模式的准确预报都具有非常重要的科学意义和实用价值。对风应力拖曳系数的参数化是风应力参数化的主要内容。近来的观测发现,风应力拖曳系数随着风速的增加出现了先增后减的趋势,同时还与海面的波浪状态以及海流有关。基于观测或理论分析,目前已经得到了一系列的风应力拖曳系数计算方法或公式,有的考虑了海浪的作用,有的没有,但这些方案大都是适合中低风速,在高风速下的适用性还有待检验。本文回顾了目前在海气动量通量观测和参数化方面的研究进展,并建议应增加高风速下风速、海流以及海浪等的同步观测,以进一步完善风应力参数化方案。     

A note on a critical wind speed for air–sea boundary processes

Wind and wind-generated waves were measured in a wind-wave tank. A clear transition was found in the relation between the wind speed U ₁₀ and the wind friction velocity u _* near u _* = 0.2 m/s, where U ₁₀ is the wind speed at 10 m height extrapolated from the measured wind profile in a logarithmic layer, and u _* = 0.2 m/s corresponds roughly to U ₁₀ = 8 m/s in the present measurement. Quite a similar transition was found in the relation between the spectral density of high frequency wind waves and u _*. These results suggest the existence of the critical wind speed for air–sea boundary processes, which was proposed by Munk (J Marine Res 6:203–218, 1947) more than half a century ago. His original idea of the critical wind speed was based on the discontinuities in such phenomena as white caps, wind stress, and evaporation, which commonly appear at a wind speed near 7 m/s. On the basis of the results of our present study and those of earlier studies, we discuss the phenomena which are relevant to the critical wind speed for the air–sea boundary processes. The conclusion is that the critical wind speed exists and it is attributed to the start of wave breaking rather than the Kelvin–Helmholtz instability, but the air–sea boundary processes are not discontinuous at a particular wind speed; because of the stochastic nature of breaking waves, the changes occur over a range of wind speeds. Detailed discussions are presented on the dynamical processes associated with the critical wind speed such as wind-induced change of sea surface roughness and high frequency wave spectrum. Future studies are required, however, to clarify the dynamical processes quantitatively. In particular, there is a need to further examine the gradual change of breaking patterns of wind waves with the increase of wind speed, and the associated change of the structure of the wind over wind waves, such as separation of the airflow at the crest of wind waves, the turbulent stress, and wave-induced stress. Studies on the dynamical structure of the high frequency wave spectrum are also needed.     

Wind gust spectrum over waves: Effect of wave age

The effect of wave age on the wind gust spectrum over wind waves is considered by using the Ochi and Shin [1988. Wind turbulent spectra for design considerations of offshore structures. Proceedings of 20th Offshore Technology Conference, Paper No. 5736, Houston, Texas. pp. 461–467] spectrum together with the wave age dependant Volkov [2001. The dependence on wave age. In: Jones, I.S.F., Toba, Y. (Eds.), Wind Stress Over the Ocean. Cambridge University Press, Cambridge, UK, pp. 206–217] sea surface roughness formula. The wave age independent Charnock [1955. Wind stress on a water surface. Quarterly Journal of Royal Meteorological Society 81, 639–640] sea surface roughness is used as a reference. An example of results demonstrates a clear effect of wave age on the wind gust spectrum.     

海面粗糙度方案的适用性研究

由量纲分析导出海面粗糙度与波龄及海面涌浪的状况有关,并对与波龄和波陡有关的两种海面粗糙度模型方案进行了敏感性测试,得出利用波龄模型方案计算粗糙度的误差比利用波陡模型方案小。基于国际上6个不同水深、风区和海况条件的海气交换试验资料,将其分为两组,一组是纯风海或以风海为主海况条件,另一组是以涌浪为主海况条件,测试波龄、波陡模型海面粗糙度方案在不同试验条件下的适用性。结果得出:在各种海况条件下,波龄模型粗糙度方案比波陡模型具有更好的普适性。在纯风海或以风海为主海况条件下,PS07,DGHQ03方案计算的粗糙度长度与实测资料计算结果最接近,GW06方案次之,O02方案计算结果明显偏高;涌浪为主海况条件下两种模型方案计算的粗糙度长度均偏低,O02方案计算的粗糙度长度误差相对较小,TY01方案误差最大。     

A study of remote sensing of sea-surface wind field with 8-12 GHz broad band radar scatterometer

The paper is devoted to the results of the study on sea-surface wind field remote sensing using 8-12 GHz broad band radar scatterometer. Principles and techniques of remote sensing with broad band scatterometer are described. Variations of microwave scattering coefficients on sea surface with different frequencies and incident angles at different polarization and wind velocity are given and the correlationship between scattering coefficients and wind speeds. The result shows that the research is valuable.lt provides data and basis for remote sensing of the sea-surface wind fields with broad band radar scatterometer.     

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42, 134–149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313–351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313–351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971–5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift.     

Wave-tide-surge coupled simulation for typhoon Maemi

The main task of this study focuses on studying the effect of wave-current interaction on currents, storm surge and wind wave as well as effects of current induced wave refraction and current on waves by using numerical models which consider the bottom boundary layer and sea surface roughness parameter for shallow and smooth bed area around Korean Peninsula. The coupled system (unstructured-mesh SWAN wave and ADCIRC) run on the same unstructured mesh. This identical and homogeneous mesh allows the physics of wave-circulation interactions to be correctly resolved in both models. The unstructured mesh can be applied to a large domain allowing all energy from deep to shallow waters to be seamlessly followed. There is no nesting or overlapping of structured wave meshes, and no interpolation is required. In response to typhoon Maemi (2003), all model components were validated independently, and shown to provide a faithful representation of the system’s response to this storm. The waves and storm surge were allowed to develop on the continental shelf and interact with the complex nearshore environment. The resulting modeling system can be used extensively for prediction of the typhoon surge. The result show that it is important to incorporate the wave-current interaction effect into coastal area in the wave-tide-surge coupled model. At the same time, it should consider effects of depth-induced wave breaking, wind field, currents and sea surface elevation in prediction of waves. Specially, we found that: (1) wave radiation stress enhanced the current and surge elevation otherwise wave enhanced nonlinear bottom boundary layer decreased that, (2) wind wave was significantly controlled by sea surface roughness thus we cautiously took the experimental expression. The resulting modeling system can be used for hindcasting (prediction) the wave-tide-surge coupled environments at complex coastline, shallow water and fine sediment area like areas around Korean Peninsula.     

Characteristics of developing waves as a function of atmospheric conditions,water properties,fetch and duration

For any specific wind speed, waves grow in period, height and length as a function of the wind duration and fetch until maximum values are reached, at which point the waves are considered to be fully developed. Although equations and nomograms exist to predict the parameters of developing waves for shorter fetch or duration conditions at different wind speeds, these either do not incorporate important variables such as the air and water temperature, or do not consider the combined effect of fetch and duration. Here, the wind conditions required for a fully developed sea are calculated from maximum wave heights as determined from the wind speed, together with a published growth law based on the friction velocity. This allows the parameters of developing waves to be estimated for any combination of wind velocity, fetch and duration, while also taking account of atmospheric conditions and water properties.